The agreement between novel exact and numerical solutions of nonlinear models
Partial Differential Equations in Applied Mathematics, 2023 Nonlinear models (NLMs), being an important topic in mathematical physics, have attracted a lot of attention in the international research community because they have numerous uses in human life. These NLMs are typically implemented to illuminate various
Md. Nur Alam, S. M. Rayhanul Islam
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Estimates for evolutionary partial differential equations in classical function spaces
Forum of Mathematics, Sigma, 2023 We establish new local and global estimates for evolutionary partial differential equations in classical Banach and quasi-Banach spaces that appear most frequently in the theory of partial differential equations.
Alejandro J. Castro +3 more
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WKB analysis for the Gross-Pitaevskii equation with non-trivial boundary conditions at infinity [PDF]
, 2007 We consider the semi-classical limit for the Gross-Pitaevskii equation. In order to consider non-trivial boundary conditions at infinity, we work in Zhidkov spaces rather than in Sobolev spaces.
Abdullaev +26 more
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Alexandria Engineering Journal, 2020 In this research, analytical and numerical solutions are studied of a two–dimensional discrete electrical lattice, which is mathematically represented by the modified Zakharov–Kuznetsov equation.
Choonkil Park +4 more
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On the continuous resonant equation for NLS: II. Statistical study [PDF]
, 2015 We consider the continuous resonant (CR) system of the 2D cubic nonlinear Schr{\"o}dinger (NLS) equation. This system arises in numerous instances as an effective equation for the long-time dynamics of NLS in confined regimes (e.g. on a compact domain or
Germain, Pierre +2 more
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Global infinite energy solutions for the cubic wave equation [PDF]
, 2015 International audienceWe prove the existence of infinite energy global solutions of the cubic wave equation in dimension greater than 3.
Burq, Nicolas +2 more
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Low regularity well-posedness of KP-I equations: the three-dimensional case [PDF]
, 2022 In this paper, low regularity local well-posedness results for the Kadomtsev–Petviashvili–I equation posed in spatial dimension $d=3$ are proved. Periodic, non-periodic and mixed settings as well as generalized dispersion relations are considered. In the
Herr, Sebastian +2 more
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Invariant Measures for Dissipative Dynamical Systems: Abstract Results and Applications [PDF]
, 2012 In this work we study certain invariant measures that can be associated to the time averaged observation of a broad class of dissipative semigroups via the notion of a generalized Banach limit.
Chekroun, Micka ël D. +1 more
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Nonlinear Schrödinger equation on four-dimensional compact manifolds [PDF]
, 2009 International ...
Gérard, Patrick, Pierfelice, Vittoria
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Multilinear Eigenfunction Estimates And Global Existence For The Three Dimensional Nonlinear Schr\"Odinger Equations [PDF]
, 2005 We study nonlinear Schr\"odinger equations, posed on a three dimensional Riemannian manifold $M$. We prove global existence of strong $H^1$ solutions on $M=S^3$ and $M=S^2\times S^1$ as far as the nonlinearity is defocusing and sub-quintic and thus we ...
Burq, N., Gerard, P., Tzvetkov, N.
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